


'''simple docstring'''




def   _a		(lowercase__			:   int = 1_0_0_0						)			->			int:






     """simple docstring"""
     __snake_case           =						-1
     __snake_case           =						0
     for a in range(1							,   n // 3						):
          # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
          __snake_case           =						(n * n - 2 * a * n) // (2 * n - 2 * a)
          __snake_case           =						n - a - b
          if c * c == (a * a + b * b):
               __snake_case           =						a * b * c
               if candidate >= product:
                    __snake_case           =						candidate
     return product


if __name__ == "__main__":
       print(f'''{solution() = }''')






"""simple docstring"""


def 						lowerCamelCase__      (				UpperCAmelCase_ = 60_08_51_47_51_43					)->				int:







       """simple docstring"""

       try:
              UpperCamelCase       			=		int(UpperCAmelCase_					)
       except (TypeError, ValueError):
              raise TypeError("Parameter n must be int or castable to int."					)
       if n <= 0:
              raise ValueError("Parameter n must be greater than or equal to one."					)
       UpperCamelCase       			=		2
       UpperCamelCase       			=		0
       if n == 2:
              return 2
       while n > 2:
              while n % i != 0:
                     i += 1
              UpperCamelCase       			=		i
              while n % i == 0:
                     UpperCamelCase       			=		n // i
              i += 1
       return int(UpperCAmelCase_					)


if __name__ == "__main__":
      print(F'''{solution() = }''')





